<p><b>Abstract</b>—This paper first shows that the bucket allocation problem of an MKH (Multiple Key Hashing) file for partial match retrieval can be reduced to that of a smaller sized subfile, called the remainder of the file. And it is pointed out that the remainder type MKH file is the hardest MKH file for which to design an optimal allocation scheme. We then particularly concentrate on the allocation of an important remainder type MKH file; namely, the k-ary MKH file. We present various sufficient conditions on the number of available disks and the number of attributes for a k-ary MKH file to have a perfectly optimal allocation among the disks for partial match queries. Based upon these perfectly optimal allocations, we further present a heuristic method, called the CH (Cyclic Hashing) method, to produce near optimal allocations for the general k-ary MKH files. Finally, a comparison, by experiment, between the performances of the proposed method and an "ideal" perfectly optimal method, shows that the CH method is indeed satisfactorily good for the general k-ary MKH files.</p>